A new lattice hierarchy: Hamiltonian structures, symplectic map and N-fold Darboux transformation

Abstract

• A new integrable lattice hierarchy is proposed. • The associated Hamiltonian structures and symplectic map are derived. • The N -fold Douboux transformations of the first two lattice systems are given. • The elastic and inelastic interaction phenomena in the lattice systems are found. A new lattice hierarchy is constructed from a discrete matrix spectral problem. By the Tu scheme technique, the associated Hamiltonian structures and infinitely many conservation laws of this hierarchy are derived. Then a symplectic map is proposed based on the Lax pair and the adjoint Lax pair. Furthermore, the N -fold Darboux transformation and explicitly exact solutions of the first two equations in the hierarchy are investigated. Finally, the density profiles of these exact solutions are presented to illustrate the overtaking collisions of solitary waves .